Measures of Center Statistics Organizing and Summarizing Data Measures of Center Questions How do the different measures of center compare? What is the difference between the sample mean and the population mean? How do you find the median of a set of values when there is an even number of values? What is the median for the following data set: 10 8 16 2 What is the median for the following data set: 10 8 16 2 100 We say that the median is a resistant measure, whereas the mean is not a resistant measure. What's a resistant measure? A course has 2 sections, Section A and Section B. On the last exam, Section A's 10 students had an average score of 80, and Section B's 20 students had an average score of 90. What is the course average score on that exam? A course has two sections, Section A and Section B. On the most recent exam, Section A's 10 students averaged 80, and Section B's 20 students averaged 90. What is the course average for this exam? Jane has scores of 84, 92, and 89 on her first 3 exams. What does she need to score on the next exam so that her overall average will be 90? The median is called a resistant measure, whereas the mean is a non-resistant measure. What's a resistant measure? The mean is the most-used measure of center, but there are times when it is recommended to use the median for data display and analysis. When might it be appropriate to use the median instead of the mean? Does a data set always have a mode? Under what conditions might the median be a preferable measure of center to use, rather than the mean? 5473ca8c581e2a3f28523bd8 What is the mode of {1,1,2,2,2,2,2,3,4,5,6,6,7,7,7,8,8,8,8,8,10,11,12,13,14,14,14} ? What will happen to the mode of a data set if you add a positive number to every value? What will happen to the median of a data set if you add a positive number to every value? Are measures of central tendency invariant to translation? What is central tendency? What is the difference between the mean, median, and mode? Are measures of central tendency invariant to translation? What do measures of central tendency indicate? What is the harmonic mean? What is an interquartile range? What is a unimodal distribution? What is a bimodal distribution? What is the difference between the mean and median of the following data set?: {18, 22, 28, 28, 32, 35, 43, 48, 51, 53, 56, 61} Can a continuous random variable have a median? What is the difference between mean and average? What is the mode of {2,5,6,3,2,8,9,10,2,3,1,17,20,2}? What are the mode, median, and mean of {15, 27, 29, 13, 18, 19, 15, 19, 19, 27, 15, 22, 13, 26, 20}? In a statistics class of 30 students, the mean score on the midterm was 72. In another class of 40 students, the mean score was 79. What was the mean score of the two classes combined? In a statistics class of 10 students, the mean score on the midterm was 702. In another class of 700 students, the mean score was 19. What was the mean score of the two classes combined? In a statistics class of 100 students, the mean score on the midterm was 98. In another class of 23 students, the mean score was 8. What was the mean score of the two classes combined? In a statistics class of 150 students, the mean score on the midterm was 98. In another class of 230 students, the mean score was 12. What was the mean score of the two classes combined? Given a set # {12, x ,17} #, for what x would the mean be 14? Given a set # {11, x ,-44, 1} #, for what x would the mean be 4? Given a set # {-1, x ,-4, -21} #, for what x would the mean of the set be 0? Given a set # {13, x ,-1, 11} #, for what x would the mean of the set be 3? Given a set # {-3,2,-1,x} #, for what x would the mean of the set be -5? Given a set # {-15,1,200,x,1} #, for what x would the mean of the set be -15? Given a set # {-1,2,-12,52,x} #, for what x would the mean of the set be -3? Given a set # {4,-2,-12,5,x} #, for what x would the mean of the set be -5? Given a set # {-3,x,3,4,6} #, for what x would the mean of the set be -11? Given a set # {-3,x,3,4,6,5,-3,2} #, for what x would the mean of the set be -1? Given a set # {-2,x,-3,-4,1,15,22,2} #, for what x would the mean of the set be -12? Given a set # {9,3,4,6,x,6,1,-4} #, for what x would the mean of the set be -32? Given a set # {3,6,2,-5,x,-12} #, for what x would the mean of the set be -10? Given the set: # {-2,10,-8,-14,x,7,-6} #, for what x would the mean of the set be -8? Given the set: # {-6,x,7,11,29,-4,-5} #, for what x would the mean of the set be -9? Given the set: # {5,3,6,-2,5,6,-1,x} #, for what x would the mean of the set be 0? Given the set: # {5,3,6,-1,x,3,-5,12} #, for what x would the mean of the set be 0? Given the set: # {5,x,11,-3,-12,19,10} #, for what x would the mean of the set be 0? Given the set: # {1,3,x,-2,-9,12} #, for what x would the mean of the set be 0? Given the set: # {1,13,-7,8,x,-2,-9,2} #, for what x would the mean of the set be 0? Given the set: # {-3,-7,18,x,-12,-9,2} #, for what x would the mean of the set be 0? Given the set: # {12,11,4,16,x,-19} #, for what x would the mean of the set be 0? Given the set: # {1,-11,-4,5,x,-16} #, for what x would the mean of the set be -2? Given the set: # {9,0,6,-10,2,x,3} #, for what x would the mean of the set be -2? Given the set: # {3/2,1/2,-5/4,x,-9/2} #, for what x would the mean of the set be -1? Given the set: # {2,-1/2,-3/4,x,7/2} #, for what x would the mean of the set be 1/2? Given the set: # {2,-1,-3,x,-3,2} #, for what x would the mean of the set be 3? Given the set: # {2,1,-3,x,1,2,-4} #, for what x would the mean of the set be 3? Given the set: # {-3,2,-5,1,x,7} #, for what x would the mean of the set be 3? Given the set: # {-1,6,4,11,x,-7} #, for what x would the mean of the set be 1? Given the set: # {-2,5,-6,8,x} #, for what x would the mean of the set be 1? Given the set: # {1,1,1,-5,x} #, for what x would the mean of the set be 1? How do you find the geometric mean for the pair of numbers: -18, -36? How does American obesity compare to obesity worldwide? Find the mean for the following data set? Andy has grades of 84, 65 and 76 on three math tests. What grade must he obtain on the next test to have an average of exactly 80 for the four tests? Analysis on monthly incentive of 5 salesman shows the mean & median of the incentives is $7000. The mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between the highest and the lowest? How do you find the mean, median, mode and range of 30, 34, 35, 39, 33, 32, 31, 36, 35, 37? If the median of the data below is 43, what is a possible value of x: 25, 34, 46, 43, 77, 68, x? How do you find the median of 33 35 31 30 17 4 18 1 11 19 39 6 14 20? How do you find the median of the set of data. 1, 2, 7, 9, 15, 26, 27? How do you find the mean and median of the data set: There are 28, 30, 29, 26, 31, and 30 students in a school's six Algebra l classes? How do you find the range and interquartile range for 3, 7, 4, 6, and 5? Question #691c5 Question #095e5 What is the range in the set of data below 35, 39, 25, 57 62, 46, 53, 41? How do you find the range and interquartile range for 37, 19, 13, 11, 10? How do you find the median between two numbers? What is the mean and median of 7, 9, 12, 9, 13? What is the median of the following numbers: 15, 8, 3, 5, 6, 11? How do you find the median of 2.8, 3.9, 5, 7.7? How do you find the median on a cumulative frequency graph? What is the mode of 1, 4, 7, 2, 7, 3, 8, 4, 2, 4, 9, 5, 2, 1? What's the mode of: 1, 2, 3, 4, 5? What is the mode of this set of data: 10 11 12 12 15 19 20 21 22? What is the mode of 1982, 1988, 1989, 1994, 1995, 2005? What is the mean, median, mode, and range of 2, 3, 3, 3, 3, 4, 4, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9? What is the mean, median, and mode of 14, 15, 15, 16, 17, 20, 21, 21, 21? How do you find the median of 4 numbers? How do you find the median of 6 numbers? How can a median be greater than the mean? How can the median be the greatest number in a set? How can I find the median of 25, 25, 25, 20? How do you find the mean of 26, 25, 24, 28? The purpose of measures of central tendency is to describe the variability within a data set. Is this true or false? Why? Why are measures of central tendency essential to descriptive statistics? Which measure of central tendency is most sensitive to extreme scores? Which measure of central tendency is the balance point? Which measure of central tendency is most resistant to sampling variation? Which measure of central tendency is responsive to the number of scores below or above it but not to their exact values? Which measure of central tendency is the lowest of the common measures of central tendency when the data is negatively skewed? What is the most common measure of central tendency? Why is the mode not used very much as a measure of central tendency? Why is the mean often not a good measure of central tendency for a skewed distribution? How are the measure of central tendency and measure of dispersion complementary to each other in describing data? Which measure of central tendency should be used when there is an outlier? How do you find the average of 32, 53.3, 77.1, 100, 24, 48, 36, 40? What is the average of the 3 temperatures -10Â°C, -30Â°C, and -55Â°C? What is the average of the 3 temperatures -50Â°C, -20Â°C, and 15Â°C? What is the average value of 86, 74, 79, 62, 74? How do you find the average of one number? Five numbers have an average of 90. Four of the numbers are 87, 93, 89, and 85. What is the remaining number? How do I find the average of $36,995, $32,507, and $37,286? How do I find the average of this set of numbers? How do you find the average of percentages? What's the formula to find the average of a set of numbers? How do you find the mean, median and mode of 1, 2, 3, 4, 5, 6, 7, 8, 9? How do you find the mean, median and mode of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10? How do you find the mean, median and mode of -500, 350, 475, -300, -500, 450, 425, -400? How do you find the mean, median and mode of -2, 2, 2, 3, 4, 4, 4? How do you find the mean, median and mode of 40, 40, 40, 40, 100, 100, 160, 160, 160, 160? How do you find the mean, median and mode of x, x, x, x, x+y, x+y, x+2y, x+2y, x+2y, x+2y? Katie must take five exams in a math class. If her scores on the first four exams are 76, 74, 90, and 88, what score must Katie get on the fifth exam for her overall mean to be at least 70? Katie must take five exams in a math class. If her scores on the first four exams are 76, 74, 90, and 88, what score must Katie get on the fifth exam for her overall mean to be at least 80? Katie must take five exams in a math class. If her scores on the first four exams are 76, 74, 90, and 88, what score must Katie get on the fifth exam for her overall mean to be at least 90? How to find the median of 57, 68, 70, 85, 88, 88? How does the median differ from the mode? For the set (3, 4, 5, 8, x), the mean, the median and the mode all have the same value. What is the value of x? What does range mean in math? What is the mode of the numbers: 153, 157, 163, 165, 166, 169, 170, 173, 176, 185? What is the mode for these numbers: 68, 68, 69, 69, 72, 73, 75, 75, 76, 84, 84, 86, 87, 88, 88, 91, 92, 92, 93, 94, 95? How do you find the mean, median, and mode of 2, 5, 5, 6, 6, 6, 7, 7, 7, 7, 9, 10? Two new numbers are added to this data set, yet the mean does not change. What do you know about the two numbers? What is the mean, median, and mode of 14, 15, 22, 15, 2, 16, 17, 13? What is the mean, median, and mode of 6, 12, 12, 16, 24? What is the mean, median, and mode of 5, 7, 6, 6, 11? What is the mean, median, and mode of 31, 28, 30, 31, 30? What is the mean, median, and mode of 86, 90, 93, 85, 79, 92? What is the mean, median, and mode of 72, 75, 78, 72, 73? What is the mean, median, and mode of 45, 50, 47, 52, 53, 45, 51? What is the mean, median, and mode of 68, 74, 71, 69, 74, 78, 70? Anita has two sisters and three brothers. The mean of all their ages is 6 years. What will their mean age be 10 years from now? Twenty years from now? What is the mode of 12, 13, 14, 14, 15, 15, 16, 17? What are the measures of central tendency? Three numbers have a mean of 14. If two of the numbers are 12 and 17, what is the other number? How do you find the mean, median, and mode of the following frequency distribution table? How do you find the mean of $7420, $3210, $6720, $5780, $1850, $4350? How do you find the mode of 20, 45, 46, 45, 49, 45, 49? How do you find the range of 5, 0, 14, 16, 13? How do you find the range of 4, 6, 3, 4, 5, 4, 7, 3? What is the mean, median, mode, and range of 1.1, 0, 3,2.8 ,4.6? What is the mean, median, mode, and range of 7.6, 7.6, 6.1, 6, 14.3? What is the mean, median, mode, and range of 68.4, 65.7, 63.9, 79.5, 52.5? What is the mean, median, and mode of 4, 5, 7, 10? How do you find the mean, median, and mode of 26, 29, 30, 31, 33, 34, 70? How do you find the mean of 16, 19, 17, 18, 15, 14, 31, 31, 41? How do you find the mean and median of 136, 129, 128, 122, 134, 120? Tyler played 5 games of basketball. The mean was 10 points. The median was 12 points. What might each of his scores be? Six students kept track of how much time they spent reading in a week. The mean was 6 hours. The mode was 7 hours. What might each of their times be? What is the median, mode, mean, and range of 17, 19, 22, 22, 27, 31, 35, 37, 45, 98? What happens to the mean, median and mode for the data 14, 15, 22, 15, 2, 16, 17, and 13 if the outlier is eliminated? For the set of numbers 90, 100, 92, 96, 93, 100, 94, which is greatest, the mean, median, or mode? How do you write down 5 numbers where the mean, median, and mode are all 6? How do you write down 5 numbers where the mean is 7 and the median and mode are 6? Question #5c3ed The mean of 2 numbers is 8. One of the numbers is 2. What is the other number? The mean of 4 numbers is 5 and the mean of 3 different numbers is 12. What is the mean of the 7 numbers together? How do you find a set of numbers that will satisfy the following conditions? How do you find the mean of the set of numbers 7, 10, 9, 13, 6? How do you find the first and third quartiles of 14, 4, 13, 18, 8, 15, 8, 3, 11, 8? What is the mean, median, and mode of 1, 4, 5, 6, 10, 25? What is the mean and median of 3, 8, 4? The mean of eight numbers is 41. The mean of two of the numbers is 29. What is the mean of the other six numbers? What is the mode, median and mean of 5, 27, 29, 13, 18, 19, 15, 19, 19, 27, 15, 22, 13, 26, 20? What is the geometric mean between 3 and 18? What is the geometric mean of the pair of numbers 576 and 4? What is the geometric mean of the pair of numbers 2 and 7? Four numbers have a mean and median of 10, none of the numbers are 10. What are the four numbers? Whats the difference between class average and class median? What is the difference between median and mean? What is the advantages and disadvantages of mean, median and mode? What is the most common measure of central tendency? What is the average of 32, 48, 60, 74? What is the range of the data: 0.167, 0.118, 0.541, 0.427, 0.65, 0.321? What is the mean, mode median and range of 11, 12, 13, 12, 14, 11, 12? What is the range of the data: 99.7, 101.8, 103.6, 98.6, 100.2. 102.9? Question #6d09a Question #ff9eb If the mean of five numbers is 25, what is their sum? What is the geometric mean of 14 and 56?What is the answer in simplest form? Over 6 days, Dan jogged 7.5 miles, 6 miles, 3 miles, 3 miles, 5.5 miles, and 5 miles. What is the mean distance that Dan jogged each day? Question #ea27d Question #517e1 How do you find the range and interquartile range for 2, 4, 8, 3, 2? How do you find the mean of the set of integers -21, 17, 15, -25, 19? Question #be5e0 What is the interquartile range of the set of data: 67, 58, 79, 85, 80, 72, 75, 76, 59, 55, 62, 67, 80? Question #93371 The mean length of 6 rods is 44.2 cm. The mean length of 5 of them is 46 cm. How long is the sixth rod? Question #dabb6 What is the mode of 4, 9, 9, 9, 4, 6, 6, 6, 9? Question #ed2b7 Question #cf813 What is the values of the 30th and 90th percentiles of the data: 18, 9, 7, 5, 11,7, 17, 20, 19, 2, 17, 12, 5,1, 13, 12, 11, 15, 16, 20? What is the first quartile of the data set: 275, 257, 301, 218, 265, 242, 201? Maria's phone bills were $95, $67, $43, and $115. What was the mean of her phone bills? How do you find the mean, variance, and standard deviation for the data: 232, 254, 264, 274, 287, 298, 312, 342, and 398? How do you find the mean, median, and mode of the data set: 15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13? The mean age of 6 women in an office is 31 years old. The mean age of 4 men in an office is 29 years old. What is the mean age (nearest year) of all the people in the office? How do you find the median of the data set 88.6, 87.8, 85.3, 89.3, 86.8, 88.3, 85.9, 89.0, 87.4? How do you find the mean of data set 10, 0, 2, and 8? How do you find the mean, median, and mode of 4, 5, 3, 3, 1, 2, 3, 2, 4, 8, 2, 4, 4, 5, 2, 3, 6, 2? What is the interquartile range of 86, 72, 85, 89, 86, 92, 73, 71, 91, 82? Christine's test scores are 89, 94, 88, 75, and 94. What does Christine need to score on the next test to have a median score of 90? Question #8fc3c What is the mean of the following numbers: 77, 81, 75, 67, 65, 65, 60, 64, 69, 71, 65, 81? The average age of the seven P.E. teachers at Carl's school is 38. If the ages of six of them are 52, 30, 23, 28, 44, and 45, what is the age of the seventh teacher? What is the first quartile of 12, 33, 15, 22, 29, 11, 17, 19, 16, 24, 38? What is the third quartile of 24, 20, 35, 43, 28, 36, 29, 44, 21, 37? Question #dfd53 A student has earned the following scores on four 100-point math tests: 66, 70, 85, 88. What score must the student earn on the fifth to earn an average grade of 80 for those five tests? How do you find the median of 37, 54, 50, 29, 34, 41? What is the mean of 80, 86, 78, 100, 27? What is the mean of 58, 76, 40, 35, 46, 45, 0, and 100? The following data show the number of hours of sleep attained during a recent night for a sample of 20 workers: 6,5,10,5,6,9,9,5,9,5,8,7,8,6,9,8,9,6,10,8. What is the mean? What is the variance? What is the standard deviation? Which measure will be affected by an outlier the most? What is the geometric mean of #3,6# and #12#? Question #b09e5 Find the median from this data? What is the geometric mean of 81 and 4? How do I find the range of lengths in this question? Organizing and Summarizing Data View all chapters Measures of Center Measures of Variability Categorical Graphs Simple Quantitative Displays Frequency Distribution The Histogram Measuring Relative Position Boxplots Linear Transformations What is Statistics? Next